5

# Continuous random variables Xand have a joint probability density functionf(x)-2.0-1.2x-0.8yfor (x) in the first quadrant unit square [0,1]x[0,1] show that flxv) is...

## Question

###### Continuous random variables Xand have a joint probability density functionf(x)-2.0-1.2x-0.8yfor (x) in the first quadrant unit square [0,1]x[0,1] show that flxv) is a legitimate probability density function on the unit square b) find the marginal densities fx(x) and fyly) compute E[X] and var(X) set up only (you needn't evaluate) integral expressions for the following probabilities P(X+Y>1) (sketch the region in the unit square) P(Y<X) (sketch the region in the unit square P(X<0.25

Continuous random variables Xand have a joint probability density function f(x)-2.0-1.2x-0.8y for (x) in the first quadrant unit square [0,1]x[0,1] show that flxv) is a legitimate probability density function on the unit square b) find the marginal densities fx(x) and fyly) compute E[X] and var(X) set up only (you needn't evaluate) integral expressions for the following probabilities P(X+Y>1) (sketch the region in the unit square) P(Y<X) (sketch the region in the unit square P(X<0.25 Y<0.25) (sketch the "numerator" in the unit square)  #### Similar Solved Questions

##### Suppose a function f:Q ~ Q (Q is the set of rational numbers) is defined as follows: f =m+n,where m and n are integers,n #0 This function is not well-defined. Explain.
Suppose a function f:Q ~ Q (Q is the set of rational numbers) is defined as follows: f =m+n,where m and n are integers,n #0 This function is not well-defined. Explain....
##### 3_2 #Lz 1 42 +6z Ei 8=2 J? 7A1 U 4 4e in
3_ 2 #Lz 1 42 +6z Ei 8=2 J? 7A1 U 4 4e in...
##### {toun tocors 1 Mcung IrHclnsIne18tudu ealiumol 6
{toun tocors 1 M cung Ir HclnsIne 1 8 tudu ealiumol 6...
##### Figure P5.7.P5.8. Consider the problem:min. f =-2n1 - X2 s.t 91 = X2 - 1<0 92 = 4x1 + 6.2 ~ 7<0 93 = 10r + 1212 ~ 15<0 94 = n + 0.25.2 _ 1<0 95 X1<0 96 = 12<0Assume the active set is {1, 2}. That is g1 = g2 = 0, rest 0_ Are KKT conditions satisfied with this assumption ?
Figure P5.7. P5.8. Consider the problem: min. f =-2n1 - X2 s.t 91 = X2 - 1<0 92 = 4x1 + 6.2 ~ 7<0 93 = 10r + 1212 ~ 15<0 94 = n + 0.25.2 _ 1<0 95 X1<0 96 = 12<0 Assume the active set is {1, 2}. That is g1 = g2 = 0, rest 0_ Are KKT conditions satisfied with this assumption ?...
##### If 2x" +x= & has & roots @ and B , find & quadratic equation with the rootsand B
If 2x" +x= & has & roots @ and B , find & quadratic equation with the roots and B...
##### Find the general solution o the differential equationy" + 4U =* sec(21)Find particular solution of the equationy = e2 cos(41)without solving for the coefficients.
Find the general solution o the differential equation y" + 4U =* sec(21) Find particular solution of the equation y = e2 cos(41) without solving for the coefficients....
##### -{4 pointsMy NotesAsk Your Teacher(a) If you increase the length of a pendulum by a factor of 2, how does the new period TN compare to the old period 7?(b) If you decrease the length of the pendulum by 15%, how does the new period TN compare to the old period T?Additional MaterialsSeclion 11,6
-{4 points My Notes Ask Your Teacher (a) If you increase the length of a pendulum by a factor of 2, how does the new period TN compare to the old period 7? (b) If you decrease the length of the pendulum by 15%, how does the new period TN compare to the old period T? Additional Materials Seclion 11,6...
##### 1) Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 70% chance that fund B will rise in price given that fund A rises in price. There is also a 20% chance that fund B will rise in price. What is the probability that at least one of the funds will rise in price?
1) Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 70% chance that fund B will rise in price given that fund A rises in price. There is also a 20% chance that fund B will rise in price. What is the probability...
##### Find the eigenvalues of $mathrm{A}$ and a basis for each eigenspace, where $A=mid egin{array}{cc}2 & 21 \ /-1 & 5 midend{array}$
Find the eigenvalues of $mathrm{A}$ and a basis for each eigenspace, where $A=mid egin{array}{cc}2 & 21 \ /-1 & 5 midend{array}$...
##### The reaction $$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)$$ is exothermic. Does the value of $K_{p}$ increase or decrease with increasing temperature?
The reaction $$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)$$ is exothermic. Does the value of $K_{p}$ increase or decrease with increasing temperature?...
##### The smaller the curvature of a bend in a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path $y=\frac{1}{3} x^{3},$ where $x$ and $y$ are measured in miles, can safely go 30 miles per hour at $\left(1, \frac{1}{3}\right) .$ How fast can it go at $\left(\frac{3}{2}, \frac{9}{8}\right) ?$
The smaller the curvature of a bend in a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car moving on the path $y=\frac{1}{3} x^{3},$ where $x$ and $y$ are measured in miles, can safely go 30 miles per h...
##### What is the expected freezing point for a solution that contains 3.616 g of C3H6O dissolved in82.041 g of nitrobenzene?freezing point of nitrobenzene = +5.70 Â°C kf (nitrobenzene) = 7.00 Â°C/mfreezing point (Â°C): _______________
What is the expected freezing point for a solution that contains 3.616 g of C3H6O dissolved in82.041 g of nitrobenzene?freezing point of nitrobenzene = +5.70 Â°C kf (nitrobenzene) = 7.00 Â°C/mfreezing point (Â°C): _______________...
##### 1) Consider the following table for a random variable XX0.21.12.33.4d) less than 2
1) Consider the following table for a random variable X X 0 .2 1 .1 2 .3 3 .4 d) less than 2...
##### 1,00-cm-high object Dleced 4ScM the Ictt converqing [ocal ength 7,65 cm; diverging to the right the converging Find the position and height the (ina Image position ccicci-focal lenoth00 cm00 cmheightthe Imade Invertedupriqht?uprightinvertedFthc Image rcal TcalVlntun?Vlctuai
1,00-cm-high object Dleced 4ScM the Ictt converqing [ocal ength 7,65 cm; diverging to the right the converging Find the position and height the (ina Image position ccicci- focal lenoth 00 cm 00 cm height the Imade Inverted upriqht? upright inverted Fthc Image rcal Tcal Vlntun? Vlctuai...
##### The pressure p required to sink & circular plate of radius r distance d into soft ground is given approximately by the equation p = k1 exp(kzr) + k3r where k1, kz and k3 are constants that must be found. Suppose you have the following data10 12 15Use Newton's method to find k1, k2 and k3 to five decimal places_
The pressure p required to sink & circular plate of radius r distance d into soft ground is given approximately by the equation p = k1 exp(kzr) + k3r where k1, kz and k3 are constants that must be found. Suppose you have the following data 10 12 15 Use Newton's method to find k1, k2 and k3 ...
##### Which enzyme joins bits of DNA?A. DNA polymeraseB. DNA ligaseC. EndonucleaseD. Primase
Which enzyme joins bits of DNA? A. DNA polymerase B. DNA ligase C. Endonuclease D. Primase...